We can build a population growth model based on the following hypothesis:
$$\frac{dN}{dt}=\text{births}-\text{deaths}$$ $$\text{births}=aN(t), a>0$$ $$\text{deaths}=bN(t), b>0$$
We can find its solution:
$$N(t)=N_0e^{(a-b)t}$$
Aside from whether or not it is a good idea, the hypothesis about the births can be replaced by the following:
$$\text{births}=aN(t-p), a>0, p>0$$
The differential equation becomes:
$$\frac{dN}{dt}=aN(t-p)+-bN(t)$$
Can the solution to this ODE be written in closed form?
I know basic calculus.